Conventionally, a GPS positioning apparatus having high positioning accuracy reduces a multipath effect. The apparatus is disclosed in JP-A-2008-139247, which corresponds to US 2008/0158053. The GPS positioning apparatus includes an altitude information memory for storing altitude information Z0 of a mobile object, a combination calculator for obtaining a combination of GPS satellites among multiple GPS satellites, from which the apparatus can capture signals, a position calculator for measuring a three dimensional position of the mobile object in each combination of GPS satellites, a difference calculator for calculating a difference between the altitude information Z0 stored in the memory and altitude information Z obtained from the three dimensional position, and a position determination element for comparing the calculated difference with a predetermined threshold value, for selecting a combination of GPS satellites that provides the difference equal to or smaller than the threshold value, and for determining the position of the mobile object based on the three dimensional position calculated from the selected combination of GPS satellites.
Further, a method for displaying a position with high accuracy is disclosed in JP-A-2009-139281. The position is calculated with reducing cases of false detection or nondetectable cases, which are caused by the multipath effect, so that the detected position is not affected by the multipath effect. In this method, orbit information and time information transmitted from the positioning satellite are received. Based on the time information, the pseudo distance between the positioning satellite and the receiver is calculated. Based on the orbit information and the time information, the position of the positioning satellite is calculated. Based on the calculated pseudo distance and the calculated position of the satellite, the current position of the receiver is calculated. Further, estimated position of the receiver is calculated, and based on the estimated position of the receiver and the position of the satellite, an estimated pseudo distance is calculated. Based on the difference between the actual pseudo distance and the estimated pseudo distance, the error of estimated observation of the pseudo distance is calculated. The error of the estimated observation is divided by a standard variation of the error of the estimated observation, and, based on the divided result, existence of the multipath effect is determined. In this method, the error of pseudo distance is defined by a difference between the estimated pseudo distance, which is obtained from the past positioning result, and the currently calculated pseudo distance. With using the error of pseudo distance, the method determines whether the multipath effect occurs. When the multipath effect occurs, the current observation information is deleted. When the multipath effect does not occur, the current observation information is used for next process of positioning.
In JP-A-2008-139247, when the error of altitude is large, the three-dimensional or two-dimensional positioning error is also large. However, correlation between the altitude error and the positioning error is small. Accordingly, it is difficult to determine based on only the altitude information whether the calculated position is proper. Thus, it is difficult to calculate the position of the receiver with high accuracy.
In JP-A-2009-139281, it is assumed that the past positioning result is proper, and the past positioning result is used as a reference. When the object is disposed in a city center, in which the multipath effect occurs continuously, it is necessary to search the past positioning result, which can be used as the reference. This search takes much time. Therefore, the position of the mobile object during the search time is estimated by a linear estimation method. Thus, the past positioning result may include error, and the pseudo distance error may be improper.